# Updating Subjective Probability

@article{Diaconis1982UpdatingSP, title={Updating Subjective Probability}, author={Persi Diaconis and Sandy L. Zabell}, journal={Journal of the American Statistical Association}, year={1982}, volume={77}, pages={822-830} }

Abstract Jeffrey's rule for revising a probability P to a new probability P* based on new probabilities P* (Ei ) on a partition {Ei } i = 1 n is P*(A) = Σ P(A| Ei ) P* (Ei ). Jeffrey's rule is applicable if it is judged that P* (A | Ei ) = P(A | Ei ) for all A and i. This article discusses some of the mathematical properties of this rule, connecting it with sufficient partitions, and maximum entropy updating of contingency tables. The main results concern simultaneous revision on two partitions… Expand

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#### References

SHOWING 1-10 OF 43 REFERENCES

Toward an Optimization Procedure for Applying Minimum Change Principles in Probability Kinematic

- Computer Science
- 1976

“Probability kinematics” is Richard Jeffrey’s term for the study of how a rational agent ought to revise his beliefs in response to inputs from experience.1 Typically, we have P0 representing a… Expand

Two Theories of Probability

- Computer Science
- PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association
- 1978

The theory of belief functions differs from the Bayesian theory in that it uses certain non-additive set functions in the place of additive probability distributions and in that it generalizes the… Expand

A Note on Jeffrey Conditionalization

- Mathematics
- Philosophy of Science
- 1978

Bayesian decision theory can be viewed as the core of psychological theory for idealized agents. To get a complete psychological theory for such agents, you have to supplement it with input and… Expand

Rational Belief and Probability Kinematics

- Mathematics
- 1980

A general form is proposed for epistemological theories, the relevant factors being: the family of epistemic judgments, the epistemic state, the epistemic commitment (governing change of state), and… Expand

Probability kinematics: A constrained optimization problem

- Mathematics, Computer Science
- J. Philos. Log.
- 1976

The following hypothesis is made: given an appropriate measure of nearness for subjective probability functions, the probability function the individual should adopt is the one closest to his original which is consistent with the new information. Expand

Jeffrey's Rule of Conditioning

- Mathematics
- Philosophy of Science
- 1981

Richard Jeffrey's generalization of Bayes' rule of conditioning follows, within the theory of belief functions, from Dempster's rule of combination and the rule of minimal extension. Both Jeffrey's… Expand

A mathematical theory of evidence

- Computer Science
- 1976

This book develops an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions. Expand

Conditionalization, Observation, and Change of Preference

- Computer Science
- 1976

This chapter discusses the justification of condition (ii) from the point of view of a frequency interpretation of probability or reasonable degree of belief, and discusses the connection between change of belief and change of preference. Expand

Slightly More Realistic Personal Probability

- Computer Science
- Philosophy of Science
- 1967

A person required to risk money on a remote digit of π would, in order to comply fully with the theory [of personal probability] have to compute that digit, though this would really be wasteful if… Expand

Bayesian Conditionalisation and the Principle of Minimum Information

- Mathematics
- The British Journal for the Philosophy of Science
- 1980

The use of the principle of minimum information, or equivalently the principle of maximum entropy, has been advocated by a number of authors over recent years both in statistical physics as well as… Expand